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Average speed=Distance travelled/Time

A=1.21 / (6.03 x 10^-8)

A=20,066,335 m/s=20,066.335 km/s=6.7% of the speed of light.

Maybe this will help :)

ALIGN

This is very interesting Max, thanks for showing me.

I used to use align all the time but it did not work here -

There are many different versions of Latex - each one seems to have its own limitations and peculiarities. :)

You are right    IT DOES WORK!

It seems you cannot add any more latex after you finish the alignment.

That is a pity but most times it would be convenient enough just to close it and start a new latex insert.

You can use this with more than one alignment - you probably know that.  :)

\begin{align*}2x - 5y &=&  8&\qquad \mbox(1)

\\3x + 9y &=&-12&\qquad \mbox(2)\end{align*}

\(\begin{align*}2x - 5y &=& 8&\qquad \mbox(1) \\3x + 9y &=&-12&\qquad \mbox(2)\end{align*}\)

Now I need to remember to use this   

PS   I am sure your Mum is a very fine mathematician :))

Simplifying 6x + 8 = 12x + 4

Reorder the terms: 8 + 6x = 12x + 4

Reorder the terms: 8 + 6x = 4 + 12x Solving 8 + 6x = 4 + 12x

Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12x' to each side of the equation. 8 + 6x + -12x = 4 + 12x + -12x

Combine like terms: 6x + -12x = -6x 8 + -6x = 4 + 12x + -12x

Combine like terms: 12x + -12x = 0 8 + -6x = 4 + 0 8 + -6x = 4

Add '-8' to each side of the equation. 8 + -8 + -6x = 4 + -8

Combine like terms: 8 + -8 = 0 0 + -6x = 4 + -8 -6x = 4 + -8

Combine like terms: 4 + -8 = -4 -6x = -4 Divide each side by '-6'.

x = 0.6666666667

Simplifying x = 0.6666666667

-7-(-2) evaluates to -5

like in the equation if there is a problem that has two negatives next to each other then u must turn it into a +

   like in -7-(-2) u make those negatives into -7+2 which equals -5

so yeah your answers -5 lol

Solve for x:
x^2+8 x = 48

Add 16 to both sides:
x^2+8 x+16 = 64

Write the left hand side as a square:
(x+4)^2 = 64

Take the square root of both sides:
x+4 = 8 or x+4 = -8

Subtract 4 from both sides:
x = 4 or x+4 = -8

Subtract 4 from both sides:
Answer: |x = 4     or     x = -12

YES!!. x * x^2 =x^3

Add up the 2 equations.....

10x = 24

x = 2.4

Substitute the value......

5(2.4)+4y = 2

4y = 2 - 12 = -10

y = -2.5

My mom is not on this forum though XD haven't even registered but she does have great maths skills.

Perimeter of triangle = 16 + 3x + 4x - 3 = 7x + 13

Perimeter of square = Perimeter of triangle = 7x + 13

Each side of square = 7/4 x + 13/4

\(\begin{array}{rll}27x^5+8x^2&=&0\\27x^3+8&=&0 \\(3x+2)(9x^2-6x+4)&=&0\\\\ 3x_1+2 = 0&&9(x_2)^2-6x_2+4=0\\ x_1=-\frac{2}{3}&&x_2=\dfrac{-(-6)\pm\sqrt{(-6)^2-4(9)(4)}}{2(9)}\\ &&\;\;\;\;\;\!\;\;\!\!=\dfrac{6\pm6i\sqrt{3}}{18}\\ &&\;\;\;\;\;\!\;\;\!\!=\dfrac{1\pm \sqrt{3}i}{3}\end{array}\\ x_1 = -\frac{2}{3}\\x_2 = \frac{1}{3}+\frac{i}{\sqrt3}\\x_3=\frac{1}{3}-\frac{i}{\sqrt3}\)

Well was I doing something wrong or I have just found the complex solutions for you?

LOL.

y^2 + 24 y + 144

= (y+12)^2

is a square of binomial.

y^2 + 24y + 144 = y^2 + 24y + 16 + k

16 + k = 144

k = 144 - 16 = 128

\(-20 \div 8\\ = -\frac{20}{8}\\ = -2.5\)

1v1 me in maths? Great. I will go first. 

What is \((x+1)^2\)?

~Max

10 divided by 2 is 5.

Because 2 x 5 = 10

Guest #2 is wrong:

"x /8 = Q  + 2    so  x = 8(Q +2)   where Q is the quotient and 2 is the remainder"       is INCORRECT

                                x = 8(Q)  + 2   is correct

anyway , if you start with a reaminder of  2   and add 9  its like a remainder of 11....pull another '8' out of there for a remainder of '3'

Minimum 640 chips   max 800 chips

 2/3-2r=1/3r+7/3, solve for r

-2r - 1/3r =7/3 - 2/3

-2 1/3r =5/3

-7/3r =5/3 multiply both sides by - 3/7

r =5/3 x - 3/7

r= - 15/21

r= - 5/7 

.04 + (.12 - .039) 1.15 =

.04 + (0.081)1.15 =

.04 + 0.09315 =0.13315

Solve for r:
2/3-2 r = r/3+7/3

Put each term in 2/3-2 r over the common denominator 3: 2/3-2 r = 2/3-(6 r)/3:
2/3-(6 r)/3 = r/3+7/3

2/3-(6 r)/3 = (2-6 r)/3:
(2-6 r)/3 = r/3+7/3

r/3+7/3 = (r+7)/3:
(2-6 r)/3 = (r+7)/3

Multiply both sides by 3:
2-6 r = r+7

Subtract r from both sides:
2+(-6 r-r) = (r-r)+7

-6 r-r = -7 r:
-7 r+2 = (r-r)+7

r-r = 0:
2-7 r = 7

Subtract 2 from both sides:
(2-2)-7 r = 7-2

2-2 = 0:
-7 r = 7-2

7-2 = 5:
-7 r = 5

Divide both sides of -7 r = 5 by -7:
(-7 r)/(-7) = 5/(-7)

(-7)/(-7) = 1:
r = 5/(-7)

Multiply numerator and denominator of 5/(-7) by -1:
Answer: |r = (-5)/7

Expand the following:
f(n) = (n+0) (n-1) (n-2) (n-3) (n-4)

(n-3) (n-4) = (n) (n) + (n) (-4) + (-3) (n) + (-3) (-4) = n^2-4 n-3 n+12 = n^2-7 n+12:
f(n) = n n^2-7 n+12 (n-1) (n-2)

(n-1) (n-2) = (n) (n) + (n) (-2) + (-1) (n) + (-1) (-2) = n^2-2 n-n+2 = n^2-3 n+2:
f(n) = n n^2-3 n+2 (n^2-7 n+12)

 | | | | n^2 | - | 3 n | + | 2
 | | | | n^2 | - | 7 n | + | 12
 | | | | 12 n^2 | - | 36 n | + | 24
 | | -7 n^3 | + | 21 n^2 | - | 14 n | + | 0
n^4 | - | 3 n^3 | + | 2 n^2 | + | 0 n | + | 0
n^4 | - | 10 n^3 | + | 35 n^2 | - | 50 n | + | 24:
f(n) = n n^4-10 n^3+35 n^2-50 n+24

n (n^4-10 n^3+35 n^2-50 n+24) = n n^4+n (-10 n^3)+n (35 n^2)+n (-50 n)+n 24:
f(n) = n n^4-10 n n^3+35 n n^2-50 n n+24 n

n (-50) n = -50 n^2:
f(n) = n n^4-10 n n^3+35 n n^2+-50 n^2+24 n

n×35 n^2 = n^(1+2)×35:
f(n) = n n^4-10 n n^3+35 n^(1+2)-50 n^2+24 n

1+2 = 3:
f(n) = n n^4-10 n n^3+35 n^3-50 n^2+24 n

n (-10) n^3 = n^(1+3) (-10):
f(n) = n n^4+-10 n^(1+3)+35 n^3-50 n^2+24 n

1+3 = 4:
f(n) = n n^4-10 n^4+35 n^3-50 n^2+24 n

n n^4 = n^(1+4):
f(n) = n^(1+4)-10 n^4+35 n^3-50 n^2+24 n

1+4 = 5:
Answer: |f(n) = n^5 - 10n^4 + 35n^3 - 50n^2 + 24n

Previous guest is wrong. Answer is 25/8

Solution

Let x /8 = Q  + 2    so  x = 8(Q +2)   where Q is the quotient and 2 is the remainder

then   x  + 9  = 8(Q +2)  +9   so

(x  +9) /8 = {  8(Q +2) +9 }  /8

              = Q +2 +9/8

which is the quotient plus a remainder of 25/8 or 3 plus a quarter.

Use integration by parts. Your two functions are sin(at)  and 1/(1+t^2)

Integral of 1/(1+t^2) = arc tan t.

you will get  Integral = sin(at).arctan (t) - Integral (  1/(1+t^2).a cos(at) ) dt    ....keep going...

sure u can complete this.......

5a-15+9a=3a+29

    14a-15=3a+29   |-3a

    11a-15=29         |+15

         11a=44         |:11

             a=4